Baking a birthday cake is one of the nicest things you can do for someone. Don't assume that someone else will do it, or that the recipient doesn't want one, or that they won't appreciate the effort.
As a very wise woman once said, "you should never have to bake your own birthday cake."
Here are some recipes you might want to try. Note there are not a lot of chocolate, because there is so much more to the world than chocolate. And there is one that does not feed a ton, for those who have a birthday friend who is often alone.